Magic of infinity

Algebra Level 3

$y$ is real number

$\sqrt { { a }^{ 2 }+a+\sqrt { { a }^{ 2 }+a+\sqrt { { a }^{ 2 }+a+\sqrt { { a }^{ 2 }+a+\sqrt { { a }^{ 2 }+a\dots } } } } } =y$

Find $y^{2}$ when $a^{ 2 } = 10000$